When you put data out, you know your starting location/place. So just shift it.. Let say I start at address 80h. I want to shift to the right. I send data to start at 80h. Then I send clear command. Then I send data to 81h. This should work for LCD.

Since you are working with LED. It seems to me you need to shift data itself, since I don't think you have an address that you can shift. Let say you have four letters ABCD that you want to shift right. Define a matrix with ABCD and an empty space in it. Then you can send specific cells of the matrix in whatever order you like. Since we want to shift right in this example. We send cells that contain ABCD first. Then we send cell that contains empty space followed by cells that contain ABCD. Now we have shifted ABCD one space to the right. Depending on how much you are showing on LED matrix, this can be done easily and it is easy to understand. If you have large image, you might want to consider some kind of for loop.